Tapped delay lines are widely used in the electronic domain to accomplish a variety of tasks (see e.g., O. Katz and D. Sadot, “A Nonlinear Electrical Equalizer with Decision Feedback for OOK Optical Communication Systems,” IEEE Transactions on Communcations, vol. 56, no. 12 pp. 2002-2006 December 2008; Kil-Hoon Lee, Debesh Bhatta, Hyoungsoo Kim, Edwar Ciebara, Joy Laskar, “A 10 Gb/s Coherent Detection System with Feed-Forward Equalizers for Optical Duobinary Transmission,” Proceedings of the 2009 European Microwave Integrated Circuits Conference (EuMIC), pp. 286-289, 2009; Yan Ciao, Fan Zhang, Juhao Li, Liang Zhangyuan Chen, Lixin Zhu, Li Li, Anshi Xu, “Experimental demonstration of nonlinear electrical equalizer to mitigate intra-channel nonlinearities in coherent QPSK systems,” 35th European Conference on Optical Communication (ECOC), 2009; Pasandi Mohammad E. Mousa, Haghighat Javad, V. David, “Adaptive weighted channel equalizer for direct-detection optical OFDM transmission systems,” LEOS Summer Topical Meeting, p 85-86, 2009). They are practical implementations of finite impulse response (FIR) filters due to their causal and stable responses.
They are practical implementations of finite impulse response (FIR) filters due to their causal and stable responses. Furthermore, linear phase response can easily be achieved by FIR filters. The filter response is tuned by selection of the number of taps (N), relative delay of each tap, and tap weights. Their excellent properties make FIR filters desirable signal processors. Compensation of transmission impairments, channel equalization, and matched filtering can all be achieved and tuned by simply changing the number (N), the delay (T1, T7, . . . ), and the weight (α0, α1, α2, . . . ) of each tap as shown in FIG. 1 in the implementation 100 of an FIR filter using tapped delay lines (TDLs). In this manner communication and signal processing systems utilize tapped delay lines for signal and data processing and channel impairment mitigation in order to operate with maximum efficiency.
For a given input x(t), the output y(t), the frequency response of the TDL will be given by the corresponding transfer function which enables to design finite impulse response (FIR) filters by changing the number of taps, delays, and weights:
      H    ⁡          (              ⅇ                  j          ⁢                                          ⁢          w                    )        =                    Y        ⁡                  (                      ⅇ                          j              ⁢                                                          ⁢              w                                )                            X        ⁡                  (                      ⅇ                          j              ⁢                                                          ⁢              w                                )                      =                  α        0            +                        α          1                ⁢                  ⅇ                      j            ⁢                                                  ⁢                          wT              1                                          +                        α          2                ⁢                  ⅇ                      j            ⁢                                                  ⁢                          wT              2                                          +      …      +                        α          N                ⁢                  ⅇ                      j            ⁢                                                  ⁢                          wT              N                                          
Traditionally, optical TDLs have mainly suffered from a difficulty in implementation and a lack of adjustability and scalability (see e.g., Sege Doucet, Sophie LaRochelle, Morin, “Reconfigurable Dispersion Equalizer Based on Phase-Apodized Fiber Bragg Gratings”, Lightwave Technology, Journal of, vol. 27, no. 16, pp. 2899-2908, 2008; K. Hasebe, T. Sakaguchi, Y. Mada, F. Koyama, Zhao Xiaoxue, C. J. Chang-Hasnain, “Bandwidth Enhancement of Directly Modulated DFB Lasers and EML Lasers using Optical Equalizers,” IEEE Lasers and Electro-Optics Society, Proceedings of, LEOS 2008). Several methods have been demonstrated to realize tapped delay lines for high speed signal processing at microwave frequencies (see e.g., Hoang Manh Nguyen, K. Igarashi, K. Katoh, K. Kikuchi, “Bandwidth- and wavelength-tunable comb filter using PLC-based optical transversal filter,” Conference on Lasers and Electro-Optics (CLEO), 2-4 Jun. 2009, Baltimore, Md., USA; Jackson, K. P., Newton, S. A., Moslehi, B., Tur, M., Cutler, C. C., Goodman, J. W., Shaw, H. J., “Optical Fiber Delay-Line Signal Processing,” Microwave Theory and Techniques, IEEE Transactions on, vol. 33, no. 3, pp. 193-210, March 1985; Jianping Yao, “Microwave Photonics,” Lightwave Technology, Journal of, no. 3, pp. 314-335, 2009). These methods involve both electrical and optical tapped delay lines to realize filters for both coherent and incoherent systems.